What five odd integers have a sum of $30$? I've been asked the following question:
What five odd integers from the set 
$\{1, 3, 5, 7, 9, 11, 13, 15\}$
that when summed together equals to $30$? Note that any integer can be used more than once. 
If my limited knowledge of maths is correct, there should be no answer, as no odd number of odd integers summed together can give an even number.
 A: By definition, odd integers are of the form $2n+1$ where $n\in \mathbb{Z}$. Since we want the sum of $5$ odd integers to be equal to $30$ this would imply that for $a,b,c,d,e \in \mathbb{Z}$ $$(2a+1)+(2b+1)+(2c+1)+(2d+1)+(2e+1)=2(a+b+c+d+e+2)+1=30$$ which is impossible since $(a+b+c+d+e+2)\in \mathbb{Z}$ and $2(a+b+c+d+e+2)+1$ is an odd integer by definition.
A: As straightforward mathematics there is no answer.
As anyone who has ever placed hymn numbers in a hymn board will know, it is possible to turn $9$ upside down to get $6$, and if this is allowed by the wording you can get a sum of $30$.
Likewise if it is odd numbers which are chosen, but the digits rather than the numbers which are added, the set $3,5,7,9,15$ gives $3+5+7+9+1+5=30$ - again this depends on precisely how the question is worded.
A: I think this is a valid question. Normal addition base 10 you can't achieve this
since
(odd+odd)+(odd+odd)+odd=even+even+odd=even+odd= always odd
or 
(2x+1)+(2y+1)+(2z+1)+(2u+1)+(2v+1)=2(x+y+z+u+v)+5 is odd
A good answer seems to be an addition with Base 5 arithmetic
3+3+3+3+3=30?
